OD-DEAL: Dynamic Expert-Guided Adversarial Learning with Online Decomposition for Scalable Capacitated Vehicle Routing

2026-01-31

AI Summary

This work addresses the challenge of efficiently solving large-scale Capacitated Vehicle Routing Problems (CVRP), which remains difficult due to the high computational complexity of heuristic methods and the limited generalization capability of neural solvers. The authors propose the OD-DEAL framework, which uniquely integrates expert-guided adversarial learning with an online decomposition strategy. By leveraging high-fidelity knowledge distillation, OD-DEAL transfers the expert behavior of Hybrid Genetic Search (HGS) into a Graph Attention Network (GAT), enabling high-quality solutions without explicit clustering. The method supports dynamic deployment and achieves sub-second inference on CVRP instances with up to tens of thousands of nodes, delivering solution quality comparable to classical heuristics while significantly enhancing scalability and real-time performance.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Solving large-scale capacitated vehicle routing problems (CVRP) is hindered by the high complexity of heuristics and the limited generalization of neural solvers on massive graphs. We propose OD-DEAL, an adversarial learning framework that tightly integrates hybrid genetic search (HGS) and online barycenter clustering (BCC) decomposition, and leverages high-fidelity knowledge distillation to transfer expert heuristic behavior. OD-DEAL trains a graph attention network (GAT)-based generative policy through a minimax game, in which divide-and-conquer strategies from a hybrid expert are distilled into dense surrogate rewards. This enables high-quality, clustering-free inference on large-scale instances. Empirical results demonstrate that OD-DEAL achieves state-of-the-art (SOTA) real-time CVRP performance, solving 10000-node instances with near-constant neural scaling. This uniquely enables the sub-second, heuristic-quality inference required for dynamic large-scale deployment.

Problem

• Capacitated Vehicle Routing Problem
• Large-scale Optimization
• Neural Solvers
• Heuristic Generalization
• Scalability

Innovation

• adversarial learning
• knowledge distillation
• graph attention network
• online decomposition
• capacitated vehicle routing